Behavior of Biological Cells in Oscillating Electric Field Gradients:
As described in my U.S. Pat. No. 5,581,349, particles placed in a uniform electric field behave in a predictable manner—the familiar electrophoresis. If the particles carry a net charge, they move toward an electrode of opposite polarity; they do not move if they carry no net charge, even if the particles are polarizable. Polarizability is the ability of charges on or inside particles to move in response to the application of external electric fields, to form electric dipole(s). If the electric field is uniform, equal and opposite forces are exerted on each end of the resulting dipole, i.e., polarizability does not influence electrophoresis.
If the electric field possesses a spatial gradient, unequal forces will be experienced by each end of the dipole, leading the particle to undergo net translational motion in the direction of the maximum in the field gradient (dielectrophoresis), even if the polarizable particle is, overall, electrically neutral. Furthermore, when the applied field gradient is oscillating at certain frequencies (typically in the radio frequency (RF) range, the particle continues the translational motion in the same direction, as illustrated in FIGS. 1A and 1B, where a field gradient is formed by the choice of shape/geometry of electrodes (11 and 12). The field gradient is imposed on polarizable cells (13 and 15), forcing motion of the cells toward the anode 12 (FIG. 1A). When the polarity of the electric field is reversed (FIG. 1B), where now electrode 12 is cathode, the polarizable cells (13 and 15) experience a similar effect, but keep moving toward maximum field gradient, i.e., the cells do not reverse direction with reversal of field polarity.
Dielectrophoresis depends on biological cell conditions, particularly changes in the dielectric properties of cells, and has been the subject of numerous studies, see [5], for review. In the treatment of the effect of oscillating electric fields on biological systems, a great number of studies have focused on the detection, by electrical means, of the changes in the electrical properties of the biomolecules.
Many neutral and charged particles (e.g., biological cells) are polarizable; polarization can occur through movement of electrically charged constituents: inside the cell, on the cell surface, or by influencing the electrical double layer surrounding the cell[1,2]. For these reasons, and because they contain numerous charged molecules, most biological cells are polarizable. Furthermore, the motion is frequency-dependent, and is maximized at certain frequencies. These properties present unique and advantageous applications in the present invention, as the motion of a particular population of cells can be selected to “resonate” at certain frequencies. The motion is maximized when the frequency matches the (inverse of) the time it takes for charges to rearrange (relaxation time).
As described in my U.S. Pat. No. 5,581,349, the force exerted by the electric field on the cell depends on several factors including intrinsic properties of the cell such as size, shape, and polarizability. The force also depends on external (experimental) factors such as the field strength, gradient, and the properties of the suspending medium. The force F can be represented as:F=2πr3g∈m∇E2   (1)
Where r is the particle's radius, ∈m is medium's dielectric constant, and E is the electric field strength. Equation 1 indicates that the force is proportional to the volume of the cell. It can be seen that the force depends on both the field strength and on the field gradient, as ∇E2 may also be written as 2E∇E. g is a function of the electrical permittivities of the particle and the medium:
                    g        =                              g            ⁡                          (                                                ɛ                  m                  *                                ,                                  ɛ                  p                  *                                            )                                =                      Re            ⁢                                          (                                                      ɛ                    p                    *                                    -                                      ɛ                    m                    *                                                  )                                            (                                                      ɛ                    p                    *                                    +                                      2                    ⁢                                                                                  ⁢                                          ɛ                      m                      *                                                                      )                                                                        (        2        )            
Where Re is the real part of the complex function, and ∈p* and ∈m* are the complex permittivities of the particle, p, and the medium, m, respectively. A force of sufficient magnitude that acts upon a particle causes particle movement, the speed of which indicates the magnitude of the force.
As can be seen from Equation 2, the direction of motion above is for the case where the absolute values of ∈*p>∈*m, (where the particles are more polarizable than the medium). In instances, such as here, where the particle is more polarizable than the medium, the particles migrate toward the minimum in the field gradient.
Dynamic Light Scattering:
To study the force in a quantitative manner (as manifested by the resulting velocity of the particle movement), dynamic light scattering (DLS) can be employed. In DLS, a light beam, typically from a laser, impinges on a solution of particles, and the intensity of the scattered light is measured at a specified angle. The frequency of the scattered light is Doppler shifted due to the Brownian motion of the scattering particle. The frequency shifts are related to the diffusion coefficients of the particles in the medium. DLS experiments measure the Fourier transform (FT) of these frequency shifts[3] as the time-domain autocorrelation function, C(τ).C(τ)=N2e−q2Dτ   (3)
Where <N> is the average number of particles per unit volume, θ is the angle between the incident and the scattered beam (defined by detector position), D is the diffusion coefficient, τ is the delay time, and q is an experimental constant related to the light arrangement and the medium:
                    q        =                                            4              ⁢                                                          ⁢              π              ⁢                                                          ⁢              n                        λ                    ⁢          sin          ⁢                                          ⁢                      θ            2                                              (        4        )            
Here, n is the refractive index of the medium, θ is the scattering angle, and λ is the wavelength of the light beam. The diffusion coefficient D for a spherical particle is:
                    D        =                  kT                      6            ⁢                                                  ⁢            π            ⁢                                                  ⁢            η            ⁢                                                  ⁢            r                                              (        5        )            
where k is the Boltzmann constant, T is the absolute temperature, η is the viscosity of the medium and r is the particle's radius. Formula (5) is presented for reference even though particles such as red blood cells are not spherical. Similar relationships exist for non-spherical particles
It is known that time autocorrelation functions of Brownian motion are smooth exponential functions and are characteristic of the diffusion coefficients of the scattering species, which are used as a measure of their size from the diffusion coefficient. Except for single (monodisperse) systems, C(τ) data will be a superposition of multiple exponentials. This drawback has historically restricted DLS from application to complex mixtures such as blood.
Dielectrophoretic Dynamic Light Scattering (DDLS):
The imposition of an oscillating electric field gradient on the particles introduces significant features into DLS. A directed (non-Brownian) motion introduces modulations into the exponentially decaying C(τ) measured in DLS experiments which adds new information. The resulting function C′(τ) is modulated since it incorporates sinusoidal (or other) OSCILLATIONS ONTO C(τ)[4]:C′(τ)=C(τ)cos(q·vτ)   (6)
where v is the directed velocity exhibited by the particle under the application of the field gradient. Equation 6 analyses may be simplified by the FT after removal of the component of the spectrum due to the Brownian motion, C(τ). C(τ) is acts as a background dampening factor for the oscillation. Removing C(τ) produces new “v-space” spectrum. The new spectrum, henceforth DDLS, provides both qualitative and quantifiable means to measuring cell movement, and thus to cell's state, and can be used to predict changes in cell due to size, shape, membrane structure, and electrical charge distribution, and, particularly in the case of cancer cells, chromosomal disorder.
The present invention utilizes discernible spectral features of Equation 6 as a function of conditions of cancer cells as predicted from Equations 1, 3, and 6. The v-space spectrum can be utilized to indicate cell state.
Additionally, the peaks in the FT spectrum may be also assigned to particular species. Each polarizable population present would, in principal, contribute a peak in the spectrum. By choice of frequency, electrode configuration and other experimental embodiments, it is possible to achieve an experimentally distinguishable response from different constituents in a mixture as described in my U.S. Pat. No. 5,581,349.
The present invention presents significant advantages for the measurement and monitoring of cells, among them the detection scheme and the use of dynamically differentiated light scattering signal. This can be revealed from examining the parameters of equations 3 and 6. An important practical characteristic of these equations is that the “static” scattering, e.g., time-invariant scattering, can be removed using appropriate logic and data analysis tools without removing significant details from collected data.
The ability to target and identify the response of a particular population of cells is an important advantage of the present invention. This is accomplished through the response of cells to the particular frequency of the applied field gradient since many cell populations respond to particular frequency ranges. This enables the targeting of a particular cell population to be preferentially affected by the choice of the applied oscillating field gradient frequency. This contrasts prior art techniques which sums the response from all components in the sample and thus renders such prior art techniques susceptible to interfering biological material.
Another advantage of the present invention can be seen from the penetration of electric fields into dielectric material, e.g., skin, finger nails, and the like which enables non-invasive characterization of diseases caused by, or manifested in, changes in cell conditions. Additionally, no reagents may be consumed by application of the present invention.
Several drawings and illustrations have been presented to aid in understanding the present invention. The scope of the present invention is not limited to what is shown in the Figures.